答案是4/3
由于分子和分母都有導(dǎo)致分式變?yōu)?的因子,所以分子和分母要分別有理化,消除根號(hào)
lim[x→4] [√(2x+1)-3]/(√x-2)
=lim[x→4] {[√(2x+1)-3][√(2x+1)+3](√x+2)}/{(√x-2)(√x+2)[√(2x+1)+3]},分子有3項(xiàng),分母有3項(xiàng),這里乘以一項(xiàng)再除以一項(xiàng),別忘了只乘而沒(méi)有除
=lim[x→4] [(2x+1-9)(√x+2)]/{(x-4)[√(2x+1)+3]}
=lim[x→4] [2(x-4)(√x+2)]/{(x-4)[√(2x+1)+3]}
=2lim[x→4] (√x+2)/[√(2x+1)+3]
=2·(√4+2)/[√(2·4+1)+3]
=2·4/6
=4/3